International System of Units

The International System of Units consists of a set of seven defining constants with seven corresponding base units, derived units, and a set of decimal-based multipliers that are used as prefixes. Twenty-two coherent derived units have been provided with special names and symbols as shown in the table below. The radian and steradian have no base units but are treated as derived units for historical reasons. Prefixes Like all metric systems, the SI uses metric prefixes to systematically construct, for the same physical quantity, a set of units that are decimal multiples of each other over a wide range. For example, driving distances are normally given in kilometres (symbol ) rather than in metres. Here the metric prefix 'kilo-' (symbol 'k') stands for a factor of 1000; thus, = . The SI provides twenty-four metric prefixes that signify decimal powers ranging from 10−30 to 1030, the most recent being adopted in 2022. Most prefixes correspond to integer powers of 1000; the only ones that do not are those for 10, 1/10, 100, and 1/100. The conversion between different SI units for one and the same physical quantity is always through a power of ten. This is why the SI (and metric systems more generally) is called decimal systems of measurement units. The grouping formed by a prefix symbol attached to a unit symbol (e.g. , ) constitutes a new inseparable unit symbol. This new symbol can be raised to a positive or negative power. It can also be combined with other unit symbols to form compound unit symbols. The BIPM specifies 24 prefixes for the International System of Units (SI): Coherent and non-coherent SI units The base units and the derived units formed as the product of powers of the base units with a numerical factor of one form a coherent system of units. Every physical quantity has exactly one coherent SI unit. For example, is the coherent derived unit for velocity. With the exception of the kilogram (for which the prefix kilo- is required for a coherent unit), when prefixes are used with the coherent SI units, the resulting units are no longer coherent, because the prefix introduces a numerical factor other than one. For example, the metre, kilometre, centimetre, nanometre, etc. are all SI units of length, though only the metre is a SI unit. The complete set of SI units consists of both the coherent set and the multiples and sub-multiples of coherent units formed by using the SI prefixes. The kilogram is the only coherent SI unit whose name and symbol include a prefix. For historical reasons, the names and symbols for multiples and sub-multiples of the unit of mass are formed as if the gram were the base unit. Prefix names and symbols are attached to the unit name gram and the unit symbol g respectively. For example, is written milligram and , not microkilogram and . The same coherent SI unit may be used for different physical quantities. For example, the joule per kelvin (symbol ) is the coherent SI unit for two distinct quantities, heat capacity and entropy, and the ampere is the coherent SI unit for both electric current and magnetomotive force. Furthermore, the same coherent SI unit may be a base unit in one context, but a coherent derived unit in another. For example, the ampere is a base unit when it is a unit of electric current, but a coherent derived unit when it is a unit of magnetomotive force. == Lexicographic conventions ==

'2'. Unit names The SI standard is that unit names are treated as common nouns of the context language. interprets the international standard by clarifying some language-specific details for American English. For example, since 1979, the litre may exceptionally be written using either an uppercase "L" or a lowercase "l", a decision prompted by the similarity of the lowercase letter "l" to the numeral "1", especially with certain typefaces or English-style handwriting. NIST recommends that within the United States, "L" be used rather than "l". == Realisation of units ==

used for measuring the Avogadro constant to a relative standard uncertainty of or less, held by Achim Leistner Metrologists carefully distinguish between the definition of a unit and its realisation. The SI units are defined by declaring that seven defining constants) describing the current best practical realisations of the unit. The separation of the defining constants from the definitions of units means that improved measurements can be developed leading to changes in the as science and technology develop, without having to revise the definitions. The published is not the only way in which a base unit can be determined. These methods include the following: • At least three separate experiments be carried out yielding values having a relative standard uncertainty in the determination of the kilogram of no more than and at least one of these values should be better than . Both the Kibble balance and the Avogadro project should be included in the experiments and any differences between these be reconciled. • The definition of the kelvin measured with a relative uncertainty of the Boltzmann constant derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry be better than one part in and that these values be corroborated by other measurements. == Organisational status ==

(SI), imperial, and US customary systems as of 2019 The International System of Units, or SI, is a decimal and metric system of units established in 1960 and periodically updated since then. The SI has an official status in most countries, including the United States, Canada, and the United Kingdom, although these three countries are among the handful of nations that, to various degrees, also continue to use their customary systems. Nevertheless, with this nearly universal level of acceptance, the SI "has been used around the world as the preferred system of units, the basic language for science, technology, industry, and trade." International System of Quantities The quantities and equations that provide the context in which the SI units are defined are now referred to as the International System of Quantities (ISQ). The ISQ is based on the base quantities underlying each of the seven base units of the SI. Derived quantities, such as area, pressure, and electrical resistance, follow from these base quantities by clear, non-contradictory equations. The ISQ defines the quantities that are measured with the SI units. The ISQ is formalised, in part, in the international standard ISO/IEC 80000, which was completed in 2009 with the publication of ISO 80000-1, and has largely been revised in 2019–2020. Controlling authority The SI is regulated and continually developed by three international organisations that were established in 1875 under the terms of the Metre Convention. They are the General Conference on Weights and Measures (CGPM), the International Committee for Weights and Measures (CIPM), and the International Bureau of Weights and Measures (BIPM). All the decisions and recommendations concerning units are collected in a brochure called The International System of Units (SI), The brochure leaves some scope for local variations, particularly regarding unit names and terms in different languages. For example, the United States' National Institute of Standards and Technology (NIST) has produced a version of the CGPM document (NIST SP 330), which clarifies usage for English-language publications that use American English. == History ==

the Austro-Hungarian/Italian border at Pontebba displaying myriametres, a unit of 10 km used in Central Europe in the 19th century (but since deprecated) CGS and MKS systems The concept of a system of units emerged a hundred years before the SI. In the 1860s, James Clerk Maxwell, William Thomson (later Lord Kelvin), and others working under the auspices of the British Association for the Advancement of Science, building on previous work of Carl Gauss, developed the centimetre–gram–second system of units or cgs system in 1874. The systems formalised the concept of a collection of related units called a coherent system of units. In a coherent system, base units combine to define derived units without extra factors. The General Conference on Weights and Measures (French: – CGPM), which was established by the Metre Convention, Initially the convention only covered standards for the metre and the kilogram. This became the foundation of the MKS system of units. for electrical distribution systems. Attempts to resolve the electrical units in terms of length, mass, and time using dimensional analysis was beset with difficulties – the dimensions depended on whether one used the ESU or EMU systems. This anomaly was resolved in 1901 when Giovanni Giorgi published a paper in which he advocated using a fourth base unit alongside the existing three base units. The fourth unit could be chosen to be electric current, voltage, or electrical resistance. Electric current with named unit 'ampere' was chosen as the base unit, and the other electrical quantities derived from it according to the laws of physics. When combined with the MKS the new system, known as MKSA, was approved in 1946. This working document was Practical system of units of measurement. Based on this study, the 10th CGPM in 1954 defined an international system derived from six base units: the metre, kilogram, second, ampere, degree Kelvin, and candela. The 9th CGPM also approved the first formal recommendation for the writing of symbols in the metric system when the basis of the rules as they are now known was laid down. These rules were subsequently extended and now cover unit symbols and names, prefix symbols and names, how quantity symbols should be written and used, and how the values of quantities should be expressed. and in 1960, the 11th CGPM adopted the International System of Units, abbreviated SI from the French name , which included a specification for units of measurement. During the 2nd and 3rd Periodic Verification of National Prototypes of the Kilogram, a significant divergence had occurred between the mass of the IPK and all of its official copies stored around the world: the copies had all noticeably increased in mass with respect to the IPK. During extraordinary verifications carried out in 2014 preparatory to redefinition of metric standards, continuing divergence was not confirmed. Nonetheless, the residual and irreducible instability of a physical IPK undermined the reliability of the entire metric system to precision measurement from small (atomic) to large (astrophysical) scales. By avoiding the use of an artefact to define units, all issues with the loss, damage, and change of the artefact are avoided. • In addition to the speed of light, four constants of nature – the Planck constant, an elementary charge, the Boltzmann constant, and the Avogadro constant – be defined to have exact values • The International Prototype of the Kilogram be retired • The current definitions of the kilogram, ampere, kelvin, and mole be revised • The wording of base unit definitions should change emphasis from explicit unit to explicit constant definitions. The new definitions were adopted at the 26th CGPM on 16 November 2018, and came into effect on 20 May 2019. The change was adopted by the European Union through Directive (EU) 2019/1258. Prior to its redefinition in 2019, the SI was defined through the seven base units from which the derived units were constructed as products of powers of the base units. After the redefinition, the SI is defined by fixing the numerical values of seven defining constants. This has the effect that the distinction between the base units and derived units is, in principle, not needed, since all units, base as well as derived, may be constructed directly from the defining constants. Nevertheless, the distinction is retained because "it is useful and historically well established", and also because the ISO/IEC 80000 series of standards, which define the International System of Quantities (ISQ), specifies base and derived quantities that necessarily have the corresponding SI units. == Related units ==

Non-SI units accepted for use with SI Many non-SI units continue to be used in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture, and their use has not been entirely replaced by their SI alternatives. The CIPM recognised and acknowledged such traditions by compiling a list of non-SI units accepted for use with SI, listed as being accepted for use alongside SI units, or for explanatory purposes. The SI prefixes can be used with several of these units, but not, for example, with the non-SI units of time. Others, in order to be converted to the corresponding SI unit, require conversion factors that are not powers of ten. Some common examples of such units are the customary units of time, namely the minute (conversion factor of , since ), the hour (), and the day (); the degree (for measuring plane angles, and the electronvolt (a unit of energy, ). other metric systems exist, some of which were in widespread use in the past or are even still used in particular areas. There are also individual metric units such as the sverdrup and the darcy that exist outside of any system of units. Most of the units of the other metric systems are not recognised by the SI. Unacceptable uses Unit symbols should not include any information about a particular value. For example, the information that a voltage reading is a maximum value should be associatied with the value, not with the unit. Thus, U_\textrm{max} = 1000\ \textrm{V} is acceptable but U = 1000\ \textrm{V}_\textrm{max} is unacceptable. A more subtle example is mass fraction. A silicon sample with small amounts of copper should be reported as with no units, for example, w(\textrm{Cu}) = 1.3 \times 10^{-6}. == See also ==